A-Math - Trigonometry - Trigonometric Identities (5) (3-6cos^2 x)/(sinx-cosx)=3(sinx+cosx)

A-Math - Trigonometry - Trigonometric Identities (5)

\(\frac{{3 - 6{{\cos }^2}x}}{{\sin x - \cos x}} = 3(\sin x + \cos x)\)

Topic: Trigonometry

We will start manipulating from the side that looks more complicated,
in this case,it is the left hand side (LHS). If you look at the question, you
realize that \(3 - 6{\cos ^2}x\) looks somewhat similar to the double angle
formula \(2{\cos ^2}x - 1 = \cos 2x\) and we can change the numerator
\(2{\cos ^2}x - 1 = \cos 2x = {\sin ^2}x - {\cos ^2}x\) to cancel out
\(\sin x - \cos x\) in the denominator.

If you practice enough question on proving trigonometric identities, you
will be able to look at the question and come up with a plan to manipulate
rather quickly, it is from experience and EXPERIENCE=PRACTICE.

Additional Math (A-Maths) and Math (E-Math) Tutor in Woodlands, Chua Chu Kang,
Sembawang, Bukit Panjang, Yishun and Johor Bahru.

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I created this Blog after my students told me that there is very little information about how to solve GCE O Level Math and Additional Math (A-Math) questions on the internet. Even if they manage to find, the solution were for very basic questions. I am a Full-time Math Tutor in Singapore. I tutor mainly in Northern Singapore (Woodlands, Chua Chu Kang, Bukit Panjang, Yishun and Sembawang). I also tutor in Johor Bahru.